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DATE OF UNIT TEST:- 02/08/2020
Unit-1: BASIC MATHEMATICS USED IN PHYSICS
Unit-1: BASIC MATHEMATICS USED IN PHYSICS ALGEBRA : Quadratic Equation ( Roots of quadratic equation, Solution by Factorization and by Shridharacharya Formula, Properties of roots (real, equal, imaginary etc), Application of Quadratic equation in physics), Binomial Theorem and binomial approximation, Logarithm and Exponents ( Laws of logarithms and exponents with applications / examples), Series ( Arithmetic Progression and its general term and Sum, Sum of rst n Natural numbers, Geometrical Progression and its general term and Sum, Sum of innite GP ), Componendo & Dividendo rule. TRIGONOMETRY : Angle & its measurement (Sexagesimal and Circular system) , Trigonometricratios, Trigonometric identities , Four Quadrants & A S T C r u l e , T- r a t i o s f o r g e n e r a l a n g l e s , Addition/subtraction Formulae , Small angle Approximation, Ranges of T-functions. CO-ORDINATE GEOMETRY : Dene Origin, Axis or Axes, Co-ordinates of a point in a plane or space (2D or 3D), Distance Formula, Slope of a line and its interpretation, Graphs of commonly used functions (Straight line, Parabola, Circle, Ellipse , Hyperbola including rectangular hyperbola , Sinusoidal functions (sine and cosine functions), Exponential functions. CALCULUS: Differential calculus ( Average rate of change and Instantaneous rate of change, Differentiation of commonly used functions, Rules of differentiation including Product and Quotient rules, Application of derivatives: Increasing and Decreasing nature, Maxima and Minima with geometrical / graphical explanation ), Integral calculus ( Integration is the reverse process of differentiation, Indenite and Denite Integration, Integration of commonly used functions, Rules of Integration, Application of Integral calculus: Area under a curve and Average value of a continuous function in an interval ).
Definition of scalar and vector quantities, Graphical representation of vectors, Notation of Vectors, Angle between two vectors , Types of Vectors ( Unit vector, Null vector, Equal vectors and equality of vectors, opposite and Negative of a vector, Parallel and antiparallel vectors, Co-planar vectors, axial vectors) ,P o s i t i o n a n d d i s p l a c e m e n t v e c t o r s , Addition/subtraction of two vectors ( Triangle law, Parallelogram law ), Addition of many vectors (Polygon law ),Unit vectors and their signicance (Representation of vector in terms of unit vector in plane and in space ) , Resolution of a Vector into components i.e. Cartesian Components in two and t h re e d ime n s i o n s a n d D i re c t i o n Co s i n e s , Multiplication or Division of a Vector by a Scalar (i.e. Real number) ,Scalar (Dot) product of two Vectors and component of a vector in the direction of another vector , Vector (Cross) product of two Vectors with its geometrical interpretation and Right hand rule for direction.
UNIT, DIMENSIONS AND MEASUREMENTS
Classification of Physical Quantities according to their dependency i.e. Fundamental (or Base) and Derived quantities , Need for measurement ( Units of measurement ) , Systems of units ( FPS, CGS, MKS, SI system of units and Supplementar y units, fundamental and derived units , Some idea about Practical and Improper units) , Standards of Length, mass and time measurements, Dimensions of physical quantities, Dimensional Formulae of important physical quantities, Dimensional analysis and its applications & its limitations, SI prexes and general guidelines for using Symbols of SI units , Errors in measurement ( Systematic, Random and Least count Errors) , Accuracy and precision of measuring instruments ; Absolute Error, Relative Error, Percentage Error and Combination of Errors , Signicant gures and its rules for Arithmetic operations ( i.e. addition, subtraction, multiplication and division) ,Rounding off the uncertain digits.
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